An assessment of orbital energy corrections for the direct random phase approximation and explicit σ-functionals

Abstract

The σ-functionals developed in the Görling group [J. Chem. Phys. 154, 014104 (2021); ibid. 155, 134111 (2021)] facilitate impressive improvements over the direct random phase approximation (dRPA) and provide chemical accuracy for a broad spectrum of benchmarks concerning reaction energies and barrier heights, but struggle considerably with problems related to self-interaction. We herein assess two possible corrections to the orbital energies in the construction of the non-interacting response function for the dRPA and σ-functionals: (i) The scaling corrections of Yang and co-workers, which have been successfully applied within DFT, and (ii) the admixture of exact exchange in a post-SCF fashion similar to some double-hybrid functionals. An analysis of static shifts to the virtual orbital energies reveals the choice of corrections to be a difficult balancing act, as the effect of the corrections vastly differs between benchmark sets. Scaling corrections are found to provide substantial improvements to self-interaction problems, but seem adversarial for thermochemistry in combination with RPA. The post-SCF inclusion of exact exchange in combination with a semicanonical projection is shown to retain the accuracy of σ-functionals over a wide range of exact exchange admixtures and reduces the computational cost of the SCF calculation compared to hybrid functionals, but provides smaller improvements to self-interaction problems than scaling corrections for the most challenging cases.

Keywords:

• Random phase approximation
• σ-functionals
• self-interaction error
• scaling corrections
• post-SCF hybrid functionals

Acknowledgments

We dedicate this work to Professor Peter M. W. Gill on the occasion of his sixtieth birthday.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 Not to be confused with ‘GSC2’ from Ref. [52], in which the curvature matrix is diagonal and defined as ${\kappa }_p={\mathrm{\partial }}^{2}E/\mathrm{\partial }{n}_p^2$ for fractional occupation numbers $n_p$.

Additional information

Funding

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under Grant TRR325 ‘Assembly Controlled Chemical Photocatalysis’ (grant No. 444632635). C.O. acknowledges additional support as Max-Planck-Fellow at the MPI-FKF Stuttgart.